How Heavy is a Ten Pound Dumbbell?

                    

Chapter 1 of Moment Arm Exercise

Note:  This is the first chapter of Moment Arm Exercise, a manual I wrote in the early 2000s on biomechanics and exercises.  Dr. Doug McGuff , Fred Hahn and the late Greg Anderson, none of whom knew me personally at the time, helped find the audience for it, strictly out of their genuine interest in the material; a gesture I continue to appreciate. 

As a gesture to remember Greg, I’ll post a chapter at a time on this blog over the next year. 

For an overview/summary, see Chris Highcock's interview on Conditioning Research for text, or   a seven minute video preview  by yours truly.  Chapters, diagrams, and photos posted here may vary slightly from the original due to formatting and other changes.  Moment Arm Exercise copyright William S. DeSimone 2013.

1.0 Finding the Moment Arms in Your Workout

Give me a long enough lever and a place to stand and I will move the earth.

                                                                                                                Archimedes¹

           How heavy is a ten-pound dumbbell?

         Try this as an experiment.  I’d like you to perform a side raise with dumbbells, and you’re going to note how heavy they feel at certain points in the movement.  You don’t necessarily need to use ten pounds, because the demonstration works with any weight, but certainly no more than 15 pounds in each hand.

      Now, instead of starting the weights with a heave and letting momentum bring your arms to horizontal, perform a super-strict, excruciatingly slow, side raise.

          At the bottom, with the dumbbells directly under your shoulders, how heavy do they feel?

         At the top, with straight elbows, your shoulders down, your arms with the dumbbells held straight out to the sides, now how heavy do they feel?

      Regardless of the number on the dumbbells, they feel “heavier” at the top.  But they’re not “heavier”, they’re the same weights.  So what happened?  If not the weight, what changed?

        Part of the answer is that the Moment Arm that the weights act on changed during the movement.  The weights hanging straight down from the shoulder is approximately the same mechanically as standing on the middle of a seesaw:  there is no lever created.  Move the weights away from the body, or walk towards the end of the seesaw, and a progressively larger Moment Arm is created.

Resistance Vs. Resistance Torque

            The point of this demonstration is that, when you exercise, especially with weights, you don’t just work against Resistance; you are actually working against Resistance applied through a Moment Arm, or Resistance Torque.  Resistance is a force, in this case represented by the dumbbell.  When a force acts on a rigid bar that rotates around a fixed point, a lever is created.  The fixed point is the axis, in this case, the shoulder.  The length of the Moment Arm is not the straight line distance between the axis and the application of force.  That would simply be the length of the arm, which doesn’t change.  The Moment Arm is “the perpendicular distance between the axis and the line of force”, and this is what changes during the movement (see Figure 1.1).

Torque is the product of force and moment arm².  In this case, with fixed dumbbells, while the resistance force is constant throughout the movement, the Moment Arm increases, so the Resistance Torque provided by the exercise increases from start to finish.

                Sorry to get technical there, but this is a critical concept.  If you recognize how the Resistance Moment Arm changes in the course of a movement, then you can estimate the pattern of Resistance Torque provided by the exercise.  Where the Resistance Torque is greatest is where the exercise is hardest, mechanically; where the Resistance Torque is least is where the exercise is easiest.   These are not necessarily the same joint positions as your muscles’ weakest and strongest positions, and coordinating these two separate, independent aspects is the whole point of Moment Arm Exercise.

                So while it may be cumbersome to use the terms Resistance Force, Resistance Torque, Resistance Moment Arm, we have to distinguish between those and Muscle Force/Torque/Moment Arm.  We’ll address the Muscle side of the equation in the next chapter, and ultimately we’ll combine that with the concept of Resistance Torque to redesign exercises.  For now, we’re going to concentrate of identifying Resistance Moment Arms, their associated Torque, and their immediate effect on an exercise.

Resistance Torque Analysis

            We’ve diagrammed the positions of maximum Resistance Torque of a dozen classic movements in Figures 1.2 and 1.3 below.  A few observations.

                The position of Maximum Resistance Torque for each is pretty much the same as the so-called “sticking point”.  We’ll elaborate in a later chapter, but for now, let’s just say that the conventional approach to “sticking points”, to cheat through them, or get a “forced rep” assist through them, ie to avoid them, may help you perform more reps, but is not necessarily the most efficient, effective, or safest way to train.

                Straight limb movements, such as the side raise, the pullover, the chest flye, have a more drastic change in Moment Arm than the compound movements.  Their Moment Arms change from Zero, with the weight directly above or below the axis, to the entire arm length.  The Moment Arms for movements that don’t use the full length of the limb are more gradual in their change, since they change from Zero to about half of the limb length at maximum; in these examples, from shoulder to elbow.  Remember though that Torque is the product of moment arm and force.  You use less weight in the exercises with the more extreme moment arm; you use more weight for the ones with the more moderate moment arm.  The calculation of maximum Resistance Torque, at the maximum, for two different exercises for the same muscle would be the same, given that you work equally hard on each.

                Contrary to what you might expect, the lighter exercise isn’t necessarily safer, because it may still generate as much Resistance Torque as the heavier exercise.  Part of what you perceive at the sticking point is the abrupt change in Moment Arm and in turn Resistance Torque; you’re not building extra strength or muscle shape there.

                In fact, you may notice in watching others (and yourself), that many of the little “cheats” that sneak in, like bending your elbows during side raises, not lowering all the way in squats, locking out in presses; are to moderate the change from smaller to larger Moment Arms.

Positive-First Vs. Negative-First

                                

Probably the most important point in this analysis has to do with when the Maximum Moment Arm hits.  In Figure 1.2, all the exercises pictured conventionally start with the positive (lifting).   They either progress to or start at a Maximum Moment Arm, and then the Moment Arm decreases.  In other words, the exercise gets easier to finish the rep.

                In the gym, this means if you are unfamiliar with an exercise, or if you pick a weight that’s too heavy, you start the exercise and realize it’s too heavy before getting too far into the rep.  Preferably, ideally, you then put the weight down and get a more appropriate weight.  Or probably and less ideally, you cheat or get assistance through the sticking point and continue the set.  Either way, you know pretty quickly and adjust accordingly.

                Compare this pattern to these exercises below.

 In this group, you perform the negative phase first.  Since your muscles handle more weight lengthening than shortening³ , you can easily pick a weight that’s too heavy to lift  but entirely manageable to lower.  The real problem starts when the Maximum Moment Arm kicks in.  Remember, you don’t only work against weight, you work against weight applied through a Moment Arm.  Now, that 700 pound squat or 300 pound bench press, that you could lift off the rack and hold because of the Zero Moment Arm, becomes a lot “heavier” as your joints bend and create a Maximum Moment Arm.  It’s like a lumberjack yelling “timber”; when the cut tree is vertical, it’s not too heavy, but as it gets more horizontal, watch out!

                And it doesn’t have to be powerlifter numbers that cause the problem.  The dumbbell chest flyes and pullovers are extremely deceptive, because you conventionally start them with the weights directly over the joints (Zero Moment Arm).  But as you lower the weights, the Moment Arm expands to the full length from shoulder to hand, an enormous increase relatively speaking, so even the lightest weights now provide substantial Torque.  And coincidentally, where your muscles and joints are least capable of handling it.

Managing Resistance Torque and Other Forces

            If there is one general suggestion to take from this, it is:  wherever possible, begin the exercise at the position of Maximum Moment Arm.  If weight is manageable here, there won’t be any surprises during the rest of the movement, at least from the predictable changes in Moment Arms.

                Of course, this means redesigning the demonstrated exercises, which we’ll do.

                A few complications.  These analyses of Moment Arm and Torque only apply when the exercise is performed slowly, with as little momentum as possible in either direction.  If you heave the weight, so that momentum of the weight takes over, or if you drop the weight, for reverse momentum, the analysis gets unnecessarily complicated.  We’re also going to ignore the weight of the limb itself, and mark the line of resistance from the actual weight.  To be technically precise, we should consider the line of resistance to be the center of gravity for the weight and the limb combined; since the same general pattern would emerge, we’ll leave it as is.

                One more.  I’ve used the terms “Zero Moment Arm” to describe a position that’s mechanically easier because the line of resistance passes through the axis.  Yet, gym experience tells us that something is happening at these positions, because we feel some forces at the stretched position of a pulldown, or the standing position of a squat.

                What we feel is tension (pulling force) and compression (pushing force).  (Internally, there may also be shear, but we’re focusing on the external, resistance side.)  On the pulldown, the weight attached to the cable is trying to pull your arms out of your torso.  Your muscles, bones, tendons, and ligaments are functioning as ties, which oppose tension, not Moment Arms, opposing Torque.  The barbell on your shoulders when you stand in a squat is pressing your vertebrae between the load and the floor; here, you function as a strut, to oppose compression⁴.  Now, there is muscular work being done in these positions, but it’s by the deeper, postural muscles, not the larger, superficial, more prominent muscles that most of us go to the gym for.  Working the postural muscles isn’t necessarily a bad thing, but loads that challenge the lats and quads, large muscles designed to move limbs, are probably too heavy for the rotator cuff and erector spinae to move.  If you want to work the postural muscles dynamically, it would be safer to do separate exercises for the deep vs. superficial muscles.  MAeX will focus on working the superficial muscles dynamically, and the postural muscles statically. 

                Which leads to a second general suggestion:  when working the superficial muscles, think of them as levers (ie Moment Arms) as opposed to ties or struts; emphasize Torque instead of tension and compression.

                We’ve only explored part of the explanation of why those original dumbbells got “heavier” in the side raise.  To finish, we move on to the other side of the process, Muscle Torque.

Notes

1. Archimedes, “the first mechanic”, from Lafferty, Force and Motion, 1999, pp 12-17;  also Macauley, The Way Things Work, 1988, pp 358, 362.
2. “The point of this demonstration…torque is the product of force and moment arm.”  Definitions based on “The Biomechanics of Resistance Exercise” by Harman, Essentials of Strength and Conditioning, 1994, pp 25-27.
3. “Since your muscles can handle more weight lengthening…” generally accepted, see Harman, p 40; Brunnstrom’s, p 144;  Levangie and Norkin, p 99.
4. The explanations of tension, compression, ties, struts based on Vogel, Cat’s Paws and Catapults, 1998, pp 128-152.

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